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arXiv · 2608.29270

SHADOWBENCH: Toward Reliable Automatic Evaluation of Semantic Alignment in Autoformalization

Hojae Han·Jongyoon Kim·Sanghyeok Park·Dongwook Cheon·Yeachan Park·Myeong Jae Jeon·Sunjong Choe·Soonho Kong·Wonseok Hur·Seung-won Hwang·Donghoon Hyeon
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Abstract

Autoformalization translates informal mathematical theorems into code for proof assistants such as Lean. A central challenge is that current evaluation metrics can accept type-correct but misaligned statements or reject correct statements written in a different formulation. Inspired by Pass@$k$, we propose SA-Pass (*Semantic Alignment Pass*), which tests formal statements using auxiliary statements called *shadows* that characterize the intended statement. A generated statement receives full credit only when it compiles, implies each shadow (forward check), and is implied by their conjunction (backward check). We instantiate SA-Pass in ShadowBench, a Lean 4 full autoformalization benchmark of 178 postgraduate- to research-level problems spanning eight mathematical areas. Claude Code (Opus 4.8) with Numina-Lean-Agent reaches $61.8\%$ compile rate and $11.2\%$ SA-Pass. Across outputs generated by six agentic configurations, SA-Pass achieves $98.8\%$ binary agreement with expert judgments. An early version of ShadowBench served as the benchmark for Track 4 of the ICML 2026 AI4Math Challenge.

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Hojae Han, Jongyoon Kim, Sanghyeok Park, Dongwook Cheon, Yeachan Park, Myeong Jae Jeon, Sunjong Choe, Soonho Kong, Wonseok Hur, Seung-won Hwang, Donghoon Hyeon. 2026-09-05. SHADOWBENCH: Toward Reliable Automatic Evaluation of Semantic Alignment in Autoformalization. https://arxiv.org/abs/2608.29270

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